Properties

Label 289.10.a.i.1.15
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 289.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(148.845356651\)
Analytic rank: \(0\)
Dimension: \(52\)
Twist minimal: no (minimal twist has level 17)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q-24.0067 q^{2} -194.286 q^{3} +64.3195 q^{4} +2543.89 q^{5} +4664.15 q^{6} -1962.84 q^{7} +10747.3 q^{8} +18063.9 q^{9} +O(q^{10})\) \(q-24.0067 q^{2} -194.286 q^{3} +64.3195 q^{4} +2543.89 q^{5} +4664.15 q^{6} -1962.84 q^{7} +10747.3 q^{8} +18063.9 q^{9} -61070.2 q^{10} +18226.6 q^{11} -12496.4 q^{12} -165432. q^{13} +47121.2 q^{14} -494241. q^{15} -290939. q^{16} -433653. q^{18} +137579. q^{19} +163622. q^{20} +381352. q^{21} -437559. q^{22} +695539. q^{23} -2.08805e6 q^{24} +4.51824e6 q^{25} +3.97148e6 q^{26} +314571. q^{27} -126249. q^{28} +4.23015e6 q^{29} +1.18651e7 q^{30} +3.78840e6 q^{31} +1.48184e6 q^{32} -3.54116e6 q^{33} -4.99325e6 q^{35} +1.16186e6 q^{36} -1.18678e7 q^{37} -3.30282e6 q^{38} +3.21411e7 q^{39} +2.73399e7 q^{40} +9.83530e6 q^{41} -9.15498e6 q^{42} -3.54345e7 q^{43} +1.17233e6 q^{44} +4.59525e7 q^{45} -1.66976e7 q^{46} +5.08554e7 q^{47} +5.65252e7 q^{48} -3.65009e7 q^{49} -1.08468e8 q^{50} -1.06405e7 q^{52} +1.55202e7 q^{53} -7.55180e6 q^{54} +4.63664e7 q^{55} -2.10953e7 q^{56} -2.67297e7 q^{57} -1.01552e8 q^{58} -9.29686e7 q^{59} -3.17893e7 q^{60} +2.04285e8 q^{61} -9.09468e7 q^{62} -3.54565e7 q^{63} +1.13387e8 q^{64} -4.20841e8 q^{65} +8.50115e7 q^{66} +5.35413e7 q^{67} -1.35133e8 q^{69} +1.19871e8 q^{70} +1.33664e8 q^{71} +1.94138e8 q^{72} -4.37702e7 q^{73} +2.84906e8 q^{74} -8.77828e8 q^{75} +8.84904e6 q^{76} -3.57759e7 q^{77} -7.71600e8 q^{78} -1.37020e8 q^{79} -7.40115e8 q^{80} -4.16668e8 q^{81} -2.36113e8 q^{82} -4.10757e8 q^{83} +2.45284e7 q^{84} +8.50664e8 q^{86} -8.21856e8 q^{87} +1.95887e8 q^{88} +2.89162e8 q^{89} -1.10317e9 q^{90} +3.24717e8 q^{91} +4.47367e7 q^{92} -7.36032e8 q^{93} -1.22087e9 q^{94} +3.49986e8 q^{95} -2.87900e8 q^{96} +2.82905e8 q^{97} +8.76264e8 q^{98} +3.29243e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q + 64q^{2} + 13312q^{4} + 49152q^{8} + 341172q^{9} + O(q^{10}) \) \( 52q + 64q^{2} + 13312q^{4} + 49152q^{8} + 341172q^{9} + 156200q^{13} + 1207872q^{15} + 3407880q^{16} + 2193336q^{18} + 1185568q^{19} + 5198336q^{21} + 13827692q^{25} + 3618944q^{26} - 9167544q^{30} + 61884888q^{32} + 1635208q^{33} + 46992776q^{35} + 156027320q^{36} + 84813952q^{38} - 4635776q^{42} + 125448912q^{43} + 164193176q^{47} + 270850284q^{49} - 226223888q^{50} + 103553016q^{52} + 426167208q^{53} + 677761520q^{55} + 375214512q^{59} + 336918024q^{60} + 190014416q^{64} + 1377178928q^{66} + 311910088q^{67} + 533688136q^{69} + 1477690280q^{70} + 2757942680q^{72} + 4047975520q^{76} + 3440336432q^{77} + 3266558756q^{81} + 2072890608q^{83} + 2630025952q^{84} + 1538547296q^{86} - 1010436256q^{87} + 1873849184q^{89} - 1998451624q^{93} - 6880776704q^{94} - 4667454128q^{98} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −24.0067 −1.06095 −0.530477 0.847699i \(-0.677987\pi\)
−0.530477 + 0.847699i \(0.677987\pi\)
\(3\) −194.286 −1.38483 −0.692413 0.721502i \(-0.743452\pi\)
−0.692413 + 0.721502i \(0.743452\pi\)
\(4\) 64.3195 0.125624
\(5\) 2543.89 1.82026 0.910129 0.414326i \(-0.135982\pi\)
0.910129 + 0.414326i \(0.135982\pi\)
\(6\) 4664.15 1.46924
\(7\) −1962.84 −0.308990 −0.154495 0.987994i \(-0.549375\pi\)
−0.154495 + 0.987994i \(0.549375\pi\)
\(8\) 10747.3 0.927673
\(9\) 18063.9 0.917740
\(10\) −61070.2 −1.93121
\(11\) 18226.6 0.375352 0.187676 0.982231i \(-0.439905\pi\)
0.187676 + 0.982231i \(0.439905\pi\)
\(12\) −12496.4 −0.173967
\(13\) −165432. −1.60648 −0.803240 0.595656i \(-0.796892\pi\)
−0.803240 + 0.595656i \(0.796892\pi\)
\(14\) 47121.2 0.327824
\(15\) −494241. −2.52074
\(16\) −290939. −1.10984
\(17\) 0 0
\(18\) −433653. −0.973681
\(19\) 137579. 0.242193 0.121097 0.992641i \(-0.461359\pi\)
0.121097 + 0.992641i \(0.461359\pi\)
\(20\) 163622. 0.228668
\(21\) 381352. 0.427897
\(22\) −437559. −0.398231
\(23\) 695539. 0.518258 0.259129 0.965843i \(-0.416565\pi\)
0.259129 + 0.965843i \(0.416565\pi\)
\(24\) −2.08805e6 −1.28466
\(25\) 4.51824e6 2.31334
\(26\) 3.97148e6 1.70440
\(27\) 314571. 0.113915
\(28\) −126249. −0.0388165
\(29\) 4.23015e6 1.11062 0.555309 0.831644i \(-0.312600\pi\)
0.555309 + 0.831644i \(0.312600\pi\)
\(30\) 1.18651e7 2.67439
\(31\) 3.78840e6 0.736764 0.368382 0.929675i \(-0.379912\pi\)
0.368382 + 0.929675i \(0.379912\pi\)
\(32\) 1.48184e6 0.249819
\(33\) −3.54116e6 −0.519796
\(34\) 0 0
\(35\) −4.99325e6 −0.562441
\(36\) 1.16186e6 0.115290
\(37\) −1.18678e7 −1.04103 −0.520513 0.853854i \(-0.674259\pi\)
−0.520513 + 0.853854i \(0.674259\pi\)
\(38\) −3.30282e6 −0.256956
\(39\) 3.21411e7 2.22469
\(40\) 2.73399e7 1.68860
\(41\) 9.83530e6 0.543576 0.271788 0.962357i \(-0.412385\pi\)
0.271788 + 0.962357i \(0.412385\pi\)
\(42\) −9.15498e6 −0.453979
\(43\) −3.54345e7 −1.58059 −0.790293 0.612729i \(-0.790072\pi\)
−0.790293 + 0.612729i \(0.790072\pi\)
\(44\) 1.17233e6 0.0471532
\(45\) 4.59525e7 1.67052
\(46\) −1.66976e7 −0.549848
\(47\) 5.08554e7 1.52018 0.760092 0.649815i \(-0.225154\pi\)
0.760092 + 0.649815i \(0.225154\pi\)
\(48\) 5.65252e7 1.53694
\(49\) −3.65009e7 −0.904525
\(50\) −1.08468e8 −2.45435
\(51\) 0 0
\(52\) −1.06405e7 −0.201813
\(53\) 1.55202e7 0.270182 0.135091 0.990833i \(-0.456867\pi\)
0.135091 + 0.990833i \(0.456867\pi\)
\(54\) −7.55180e6 −0.120859
\(55\) 4.63664e7 0.683237
\(56\) −2.10953e7 −0.286641
\(57\) −2.67297e7 −0.335395
\(58\) −1.01552e8 −1.17831
\(59\) −9.29686e7 −0.998854 −0.499427 0.866356i \(-0.666456\pi\)
−0.499427 + 0.866356i \(0.666456\pi\)
\(60\) −3.17893e7 −0.316665
\(61\) 2.04285e8 1.88909 0.944543 0.328387i \(-0.106505\pi\)
0.944543 + 0.328387i \(0.106505\pi\)
\(62\) −9.09468e7 −0.781673
\(63\) −3.54565e7 −0.283572
\(64\) 1.13387e8 0.844796
\(65\) −4.20841e8 −2.92421
\(66\) 8.50115e7 0.551480
\(67\) 5.35413e7 0.324603 0.162301 0.986741i \(-0.448108\pi\)
0.162301 + 0.986741i \(0.448108\pi\)
\(68\) 0 0
\(69\) −1.35133e8 −0.717697
\(70\) 1.19871e8 0.596724
\(71\) 1.33664e8 0.624242 0.312121 0.950042i \(-0.398961\pi\)
0.312121 + 0.950042i \(0.398961\pi\)
\(72\) 1.94138e8 0.851363
\(73\) −4.37702e7 −0.180395 −0.0901977 0.995924i \(-0.528750\pi\)
−0.0901977 + 0.995924i \(0.528750\pi\)
\(74\) 2.84906e8 1.10448
\(75\) −8.77828e8 −3.20357
\(76\) 8.84904e6 0.0304253
\(77\) −3.57759e7 −0.115980
\(78\) −7.71600e8 −2.36030
\(79\) −1.37020e8 −0.395787 −0.197893 0.980224i \(-0.563410\pi\)
−0.197893 + 0.980224i \(0.563410\pi\)
\(80\) −7.40115e8 −2.02020
\(81\) −4.16668e8 −1.07549
\(82\) −2.36113e8 −0.576709
\(83\) −4.10757e8 −0.950023 −0.475011 0.879980i \(-0.657556\pi\)
−0.475011 + 0.879980i \(0.657556\pi\)
\(84\) 2.45284e7 0.0537541
\(85\) 0 0
\(86\) 8.50664e8 1.67693
\(87\) −8.21856e8 −1.53801
\(88\) 1.95887e8 0.348204
\(89\) 2.89162e8 0.488524 0.244262 0.969709i \(-0.421454\pi\)
0.244262 + 0.969709i \(0.421454\pi\)
\(90\) −1.10317e9 −1.77235
\(91\) 3.24717e8 0.496385
\(92\) 4.47367e7 0.0651057
\(93\) −7.36032e8 −1.02029
\(94\) −1.22087e9 −1.61285
\(95\) 3.49986e8 0.440854
\(96\) −2.87900e8 −0.345956
\(97\) 2.82905e8 0.324465 0.162233 0.986753i \(-0.448131\pi\)
0.162233 + 0.986753i \(0.448131\pi\)
\(98\) 8.76264e8 0.959660
\(99\) 3.29243e8 0.344475
\(100\) 2.90611e8 0.290611
\(101\) 2.20849e8 0.211179 0.105589 0.994410i \(-0.466327\pi\)
0.105589 + 0.994410i \(0.466327\pi\)
\(102\) 0 0
\(103\) −1.05360e8 −0.0922372 −0.0461186 0.998936i \(-0.514685\pi\)
−0.0461186 + 0.998936i \(0.514685\pi\)
\(104\) −1.77795e9 −1.49029
\(105\) 9.70116e8 0.778882
\(106\) −3.72588e8 −0.286651
\(107\) −4.96752e8 −0.366364 −0.183182 0.983079i \(-0.558640\pi\)
−0.183182 + 0.983079i \(0.558640\pi\)
\(108\) 2.02331e7 0.0143105
\(109\) −6.36599e8 −0.431963 −0.215982 0.976397i \(-0.569295\pi\)
−0.215982 + 0.976397i \(0.569295\pi\)
\(110\) −1.11310e9 −0.724883
\(111\) 2.30574e9 1.44164
\(112\) 5.71066e8 0.342930
\(113\) −9.53685e8 −0.550240 −0.275120 0.961410i \(-0.588718\pi\)
−0.275120 + 0.961410i \(0.588718\pi\)
\(114\) 6.41690e8 0.355839
\(115\) 1.76937e9 0.943363
\(116\) 2.72081e8 0.139520
\(117\) −2.98835e9 −1.47433
\(118\) 2.23186e9 1.05974
\(119\) 0 0
\(120\) −5.31176e9 −2.33842
\(121\) −2.02574e9 −0.859111
\(122\) −4.90419e9 −2.00423
\(123\) −1.91086e9 −0.752757
\(124\) 2.43668e8 0.0925553
\(125\) 6.52536e9 2.39061
\(126\) 8.51193e8 0.300857
\(127\) 5.40081e9 1.84222 0.921111 0.389299i \(-0.127283\pi\)
0.921111 + 0.389299i \(0.127283\pi\)
\(128\) −3.48073e9 −1.14611
\(129\) 6.88441e9 2.18884
\(130\) 1.01030e10 3.10245
\(131\) −2.76594e9 −0.820582 −0.410291 0.911955i \(-0.634573\pi\)
−0.410291 + 0.911955i \(0.634573\pi\)
\(132\) −2.27766e8 −0.0652989
\(133\) −2.70046e8 −0.0748352
\(134\) −1.28535e9 −0.344389
\(135\) 8.00233e8 0.207355
\(136\) 0 0
\(137\) −3.06041e9 −0.742228 −0.371114 0.928587i \(-0.621024\pi\)
−0.371114 + 0.928587i \(0.621024\pi\)
\(138\) 3.24409e9 0.761443
\(139\) 3.55042e9 0.806702 0.403351 0.915045i \(-0.367845\pi\)
0.403351 + 0.915045i \(0.367845\pi\)
\(140\) −3.21163e8 −0.0706561
\(141\) −9.88046e9 −2.10519
\(142\) −3.20883e9 −0.662292
\(143\) −3.01527e9 −0.602995
\(144\) −5.25548e9 −1.01855
\(145\) 1.07610e10 2.02161
\(146\) 1.05078e9 0.191391
\(147\) 7.09159e9 1.25261
\(148\) −7.63330e8 −0.130778
\(149\) −3.88137e9 −0.645130 −0.322565 0.946547i \(-0.604545\pi\)
−0.322565 + 0.946547i \(0.604545\pi\)
\(150\) 2.10737e10 3.39884
\(151\) 8.28467e9 1.29682 0.648409 0.761292i \(-0.275435\pi\)
0.648409 + 0.761292i \(0.275435\pi\)
\(152\) 1.47861e9 0.224676
\(153\) 0 0
\(154\) 8.58860e8 0.123049
\(155\) 9.63727e9 1.34110
\(156\) 2.06730e9 0.279475
\(157\) −1.15724e10 −1.52011 −0.760053 0.649861i \(-0.774827\pi\)
−0.760053 + 0.649861i \(0.774827\pi\)
\(158\) 3.28939e9 0.419912
\(159\) −3.01535e9 −0.374155
\(160\) 3.76963e9 0.454736
\(161\) −1.36523e9 −0.160136
\(162\) 1.00028e10 1.14105
\(163\) 7.06563e9 0.783983 0.391991 0.919969i \(-0.371786\pi\)
0.391991 + 0.919969i \(0.371786\pi\)
\(164\) 6.32602e8 0.0682862
\(165\) −9.00832e9 −0.946163
\(166\) 9.86091e9 1.00793
\(167\) −9.51502e9 −0.946642 −0.473321 0.880890i \(-0.656945\pi\)
−0.473321 + 0.880890i \(0.656945\pi\)
\(168\) 4.09850e9 0.396948
\(169\) 1.67633e10 1.58078
\(170\) 0 0
\(171\) 2.48522e9 0.222270
\(172\) −2.27913e9 −0.198560
\(173\) −1.34873e10 −1.14477 −0.572385 0.819985i \(-0.693982\pi\)
−0.572385 + 0.819985i \(0.693982\pi\)
\(174\) 1.97300e10 1.63176
\(175\) −8.86858e9 −0.714797
\(176\) −5.30282e9 −0.416581
\(177\) 1.80625e10 1.38324
\(178\) −6.94181e9 −0.518302
\(179\) −2.32156e10 −1.69021 −0.845107 0.534597i \(-0.820463\pi\)
−0.845107 + 0.534597i \(0.820463\pi\)
\(180\) 2.95564e9 0.209858
\(181\) −1.04604e10 −0.724425 −0.362212 0.932096i \(-0.617978\pi\)
−0.362212 + 0.932096i \(0.617978\pi\)
\(182\) −7.79537e9 −0.526642
\(183\) −3.96896e10 −2.61605
\(184\) 7.47517e9 0.480774
\(185\) −3.01903e10 −1.89493
\(186\) 1.76697e10 1.08248
\(187\) 0 0
\(188\) 3.27099e9 0.190972
\(189\) −6.17453e8 −0.0351986
\(190\) −8.40200e9 −0.467726
\(191\) 2.86896e10 1.55982 0.779909 0.625893i \(-0.215265\pi\)
0.779909 + 0.625893i \(0.215265\pi\)
\(192\) −2.20294e10 −1.16989
\(193\) −1.05634e9 −0.0548022 −0.0274011 0.999625i \(-0.508723\pi\)
−0.0274011 + 0.999625i \(0.508723\pi\)
\(194\) −6.79161e9 −0.344243
\(195\) 8.17633e10 4.04951
\(196\) −2.34772e9 −0.113630
\(197\) 1.48923e9 0.0704474 0.0352237 0.999379i \(-0.488786\pi\)
0.0352237 + 0.999379i \(0.488786\pi\)
\(198\) −7.90402e9 −0.365473
\(199\) −1.25548e10 −0.567504 −0.283752 0.958898i \(-0.591579\pi\)
−0.283752 + 0.958898i \(0.591579\pi\)
\(200\) 4.85589e10 2.14602
\(201\) −1.04023e10 −0.449518
\(202\) −5.30186e9 −0.224051
\(203\) −8.30310e9 −0.343169
\(204\) 0 0
\(205\) 2.50199e10 0.989448
\(206\) 2.52933e9 0.0978595
\(207\) 1.25641e10 0.475626
\(208\) 4.81306e10 1.78294
\(209\) 2.50760e9 0.0909076
\(210\) −2.32892e10 −0.826358
\(211\) 3.03540e10 1.05425 0.527127 0.849787i \(-0.323269\pi\)
0.527127 + 0.849787i \(0.323269\pi\)
\(212\) 9.98253e8 0.0339414
\(213\) −2.59691e10 −0.864466
\(214\) 1.19253e10 0.388695
\(215\) −9.01413e10 −2.87707
\(216\) 3.38079e9 0.105676
\(217\) −7.43603e9 −0.227652
\(218\) 1.52826e10 0.458293
\(219\) 8.50392e9 0.249816
\(220\) 2.98226e9 0.0858310
\(221\) 0 0
\(222\) −5.53530e10 −1.52951
\(223\) 2.73787e10 0.741380 0.370690 0.928757i \(-0.379121\pi\)
0.370690 + 0.928757i \(0.379121\pi\)
\(224\) −2.90862e9 −0.0771916
\(225\) 8.16169e10 2.12304
\(226\) 2.28948e10 0.583779
\(227\) −3.41868e10 −0.854560 −0.427280 0.904119i \(-0.640528\pi\)
−0.427280 + 0.904119i \(0.640528\pi\)
\(228\) −1.71924e9 −0.0421337
\(229\) 3.42397e9 0.0822753 0.0411377 0.999153i \(-0.486902\pi\)
0.0411377 + 0.999153i \(0.486902\pi\)
\(230\) −4.24767e10 −1.00087
\(231\) 6.95074e9 0.160612
\(232\) 4.54627e10 1.03029
\(233\) −3.46809e10 −0.770882 −0.385441 0.922732i \(-0.625951\pi\)
−0.385441 + 0.922732i \(0.625951\pi\)
\(234\) 7.17403e10 1.56420
\(235\) 1.29370e11 2.76713
\(236\) −5.97970e9 −0.125480
\(237\) 2.66210e10 0.548096
\(238\) 0 0
\(239\) 6.84083e10 1.35618 0.678092 0.734977i \(-0.262807\pi\)
0.678092 + 0.734977i \(0.262807\pi\)
\(240\) 1.43794e11 2.79762
\(241\) 2.87585e10 0.549148 0.274574 0.961566i \(-0.411463\pi\)
0.274574 + 0.961566i \(0.411463\pi\)
\(242\) 4.86312e10 0.911478
\(243\) 7.47609e10 1.37545
\(244\) 1.31395e10 0.237315
\(245\) −9.28541e10 −1.64647
\(246\) 4.58733e10 0.798641
\(247\) −2.27601e10 −0.389078
\(248\) 4.07151e10 0.683476
\(249\) 7.98042e10 1.31562
\(250\) −1.56652e11 −2.53633
\(251\) 5.08079e10 0.807978 0.403989 0.914764i \(-0.367623\pi\)
0.403989 + 0.914764i \(0.367623\pi\)
\(252\) −2.28055e9 −0.0356235
\(253\) 1.26773e10 0.194529
\(254\) −1.29655e11 −1.95451
\(255\) 0 0
\(256\) 2.55069e10 0.371174
\(257\) 4.43960e10 0.634811 0.317406 0.948290i \(-0.397188\pi\)
0.317406 + 0.948290i \(0.397188\pi\)
\(258\) −1.65272e11 −2.32225
\(259\) 2.32945e10 0.321666
\(260\) −2.70683e10 −0.367351
\(261\) 7.64129e10 1.01926
\(262\) 6.64010e10 0.870600
\(263\) 4.45406e10 0.574057 0.287028 0.957922i \(-0.407333\pi\)
0.287028 + 0.957922i \(0.407333\pi\)
\(264\) −3.80580e10 −0.482201
\(265\) 3.94817e10 0.491801
\(266\) 6.48291e9 0.0793967
\(267\) −5.61800e10 −0.676520
\(268\) 3.44375e9 0.0407779
\(269\) −7.75647e10 −0.903189 −0.451594 0.892223i \(-0.649145\pi\)
−0.451594 + 0.892223i \(0.649145\pi\)
\(270\) −1.92109e10 −0.219994
\(271\) 2.04736e10 0.230586 0.115293 0.993332i \(-0.463219\pi\)
0.115293 + 0.993332i \(0.463219\pi\)
\(272\) 0 0
\(273\) −6.30879e10 −0.687407
\(274\) 7.34703e10 0.787470
\(275\) 8.23521e10 0.868315
\(276\) −8.69170e9 −0.0901600
\(277\) −9.13323e10 −0.932106 −0.466053 0.884757i \(-0.654324\pi\)
−0.466053 + 0.884757i \(0.654324\pi\)
\(278\) −8.52337e10 −0.855874
\(279\) 6.84332e10 0.676158
\(280\) −5.36640e10 −0.521761
\(281\) 1.59049e11 1.52179 0.760893 0.648877i \(-0.224761\pi\)
0.760893 + 0.648877i \(0.224761\pi\)
\(282\) 2.37197e11 2.23351
\(283\) −4.93813e10 −0.457639 −0.228820 0.973469i \(-0.573487\pi\)
−0.228820 + 0.973469i \(0.573487\pi\)
\(284\) 8.59723e9 0.0784198
\(285\) −6.79973e10 −0.610506
\(286\) 7.23865e10 0.639750
\(287\) −1.93051e10 −0.167959
\(288\) 2.67678e10 0.229269
\(289\) 0 0
\(290\) −2.58336e11 −2.14484
\(291\) −5.49644e10 −0.449328
\(292\) −2.81528e9 −0.0226620
\(293\) 9.46411e10 0.750197 0.375099 0.926985i \(-0.377609\pi\)
0.375099 + 0.926985i \(0.377609\pi\)
\(294\) −1.70245e11 −1.32896
\(295\) −2.36502e11 −1.81817
\(296\) −1.27547e11 −0.965731
\(297\) 5.73356e9 0.0427583
\(298\) 9.31787e10 0.684453
\(299\) −1.15065e11 −0.832571
\(300\) −5.64615e10 −0.402445
\(301\) 6.95523e10 0.488385
\(302\) −1.98887e11 −1.37586
\(303\) −4.29079e10 −0.292446
\(304\) −4.00271e10 −0.268796
\(305\) 5.19677e11 3.43862
\(306\) 0 0
\(307\) 1.91043e11 1.22746 0.613731 0.789515i \(-0.289668\pi\)
0.613731 + 0.789515i \(0.289668\pi\)
\(308\) −2.30109e9 −0.0145699
\(309\) 2.04698e10 0.127732
\(310\) −2.31359e11 −1.42285
\(311\) −1.82343e11 −1.10526 −0.552632 0.833425i \(-0.686377\pi\)
−0.552632 + 0.833425i \(0.686377\pi\)
\(312\) 3.45430e11 2.06379
\(313\) 2.16835e11 1.27697 0.638483 0.769636i \(-0.279562\pi\)
0.638483 + 0.769636i \(0.279562\pi\)
\(314\) 2.77814e11 1.61276
\(315\) −9.01974e10 −0.516174
\(316\) −8.81305e9 −0.0497204
\(317\) 2.39301e11 1.33100 0.665499 0.746399i \(-0.268219\pi\)
0.665499 + 0.746399i \(0.268219\pi\)
\(318\) 7.23885e10 0.396961
\(319\) 7.71011e10 0.416872
\(320\) 2.88443e11 1.53775
\(321\) 9.65117e10 0.507350
\(322\) 3.27747e10 0.169897
\(323\) 0 0
\(324\) −2.67999e10 −0.135108
\(325\) −7.47462e11 −3.71633
\(326\) −1.69622e11 −0.831770
\(327\) 1.23682e11 0.598194
\(328\) 1.05703e11 0.504260
\(329\) −9.98210e10 −0.469721
\(330\) 2.16260e11 1.00384
\(331\) −2.69499e11 −1.23404 −0.617022 0.786946i \(-0.711661\pi\)
−0.617022 + 0.786946i \(0.711661\pi\)
\(332\) −2.64197e10 −0.119346
\(333\) −2.14378e11 −0.955391
\(334\) 2.28424e11 1.00434
\(335\) 1.36203e11 0.590860
\(336\) −1.10950e11 −0.474898
\(337\) 1.88865e11 0.797657 0.398828 0.917026i \(-0.369417\pi\)
0.398828 + 0.917026i \(0.369417\pi\)
\(338\) −4.02432e11 −1.67713
\(339\) 1.85287e11 0.761985
\(340\) 0 0
\(341\) 6.90496e10 0.276546
\(342\) −5.96617e10 −0.235819
\(343\) 1.50853e11 0.588479
\(344\) −3.80825e11 −1.46627
\(345\) −3.43763e11 −1.30639
\(346\) 3.23786e11 1.21455
\(347\) −1.69621e11 −0.628054 −0.314027 0.949414i \(-0.601678\pi\)
−0.314027 + 0.949414i \(0.601678\pi\)
\(348\) −5.28614e10 −0.193211
\(349\) −3.05069e11 −1.10074 −0.550369 0.834922i \(-0.685513\pi\)
−0.550369 + 0.834922i \(0.685513\pi\)
\(350\) 2.12905e11 0.758367
\(351\) −5.20402e10 −0.183002
\(352\) 2.70089e10 0.0937702
\(353\) −1.48766e10 −0.0509938 −0.0254969 0.999675i \(-0.508117\pi\)
−0.0254969 + 0.999675i \(0.508117\pi\)
\(354\) −4.33619e11 −1.46755
\(355\) 3.40027e11 1.13628
\(356\) 1.85988e10 0.0613704
\(357\) 0 0
\(358\) 5.57329e11 1.79324
\(359\) −8.13885e10 −0.258606 −0.129303 0.991605i \(-0.541274\pi\)
−0.129303 + 0.991605i \(0.541274\pi\)
\(360\) 4.93866e11 1.54970
\(361\) −3.03760e11 −0.941342
\(362\) 2.51118e11 0.768582
\(363\) 3.93572e11 1.18972
\(364\) 2.08857e10 0.0623580
\(365\) −1.11346e11 −0.328366
\(366\) 9.52814e11 2.77551
\(367\) −2.76299e11 −0.795028 −0.397514 0.917596i \(-0.630127\pi\)
−0.397514 + 0.917596i \(0.630127\pi\)
\(368\) −2.02359e11 −0.575185
\(369\) 1.77664e11 0.498861
\(370\) 7.24767e11 2.01044
\(371\) −3.04637e10 −0.0834834
\(372\) −4.73412e10 −0.128173
\(373\) 6.75562e10 0.180707 0.0903536 0.995910i \(-0.471200\pi\)
0.0903536 + 0.995910i \(0.471200\pi\)
\(374\) 0 0
\(375\) −1.26778e12 −3.31058
\(376\) 5.46558e11 1.41023
\(377\) −6.99803e11 −1.78418
\(378\) 1.48230e10 0.0373441
\(379\) 2.28533e10 0.0568948 0.0284474 0.999595i \(-0.490944\pi\)
0.0284474 + 0.999595i \(0.490944\pi\)
\(380\) 2.25110e10 0.0553819
\(381\) −1.04930e12 −2.55116
\(382\) −6.88741e11 −1.65490
\(383\) 5.41458e11 1.28579 0.642896 0.765954i \(-0.277733\pi\)
0.642896 + 0.765954i \(0.277733\pi\)
\(384\) 6.76256e11 1.58716
\(385\) −9.10098e10 −0.211113
\(386\) 2.53593e10 0.0581426
\(387\) −6.40084e11 −1.45057
\(388\) 1.81963e10 0.0407607
\(389\) −2.43923e11 −0.540107 −0.270054 0.962845i \(-0.587041\pi\)
−0.270054 + 0.962845i \(0.587041\pi\)
\(390\) −1.96286e12 −4.29635
\(391\) 0 0
\(392\) −3.92286e11 −0.839104
\(393\) 5.37382e11 1.13636
\(394\) −3.57515e10 −0.0747415
\(395\) −3.48563e11 −0.720434
\(396\) 2.11768e10 0.0432744
\(397\) −6.74857e11 −1.36350 −0.681749 0.731586i \(-0.738780\pi\)
−0.681749 + 0.731586i \(0.738780\pi\)
\(398\) 3.01398e11 0.602096
\(399\) 5.24661e10 0.103634
\(400\) −1.31453e12 −2.56744
\(401\) −3.75361e11 −0.724937 −0.362468 0.931996i \(-0.618066\pi\)
−0.362468 + 0.931996i \(0.618066\pi\)
\(402\) 2.49724e11 0.476918
\(403\) −6.26724e11 −1.18360
\(404\) 1.42049e10 0.0265291
\(405\) −1.05996e12 −1.95767
\(406\) 1.99330e11 0.364087
\(407\) −2.16309e11 −0.390751
\(408\) 0 0
\(409\) 6.31772e11 1.11636 0.558182 0.829719i \(-0.311499\pi\)
0.558182 + 0.829719i \(0.311499\pi\)
\(410\) −6.00644e11 −1.04976
\(411\) 5.94594e11 1.02786
\(412\) −6.77668e9 −0.0115872
\(413\) 1.82482e11 0.308636
\(414\) −3.01623e11 −0.504618
\(415\) −1.04492e12 −1.72929
\(416\) −2.45144e11 −0.401330
\(417\) −6.89795e11 −1.11714
\(418\) −6.01991e10 −0.0964488
\(419\) 5.81662e11 0.921951 0.460975 0.887413i \(-0.347500\pi\)
0.460975 + 0.887413i \(0.347500\pi\)
\(420\) 6.23974e10 0.0978463
\(421\) 3.73500e11 0.579457 0.289729 0.957109i \(-0.406435\pi\)
0.289729 + 0.957109i \(0.406435\pi\)
\(422\) −7.28698e11 −1.11851
\(423\) 9.18645e11 1.39513
\(424\) 1.66801e11 0.250640
\(425\) 0 0
\(426\) 6.23430e11 0.917159
\(427\) −4.00979e11 −0.583708
\(428\) −3.19508e10 −0.0460241
\(429\) 5.85823e11 0.835042
\(430\) 2.16399e12 3.05244
\(431\) 1.32118e12 1.84423 0.922113 0.386920i \(-0.126461\pi\)
0.922113 + 0.386920i \(0.126461\pi\)
\(432\) −9.15208e10 −0.126428
\(433\) 4.56730e11 0.624401 0.312201 0.950016i \(-0.398934\pi\)
0.312201 + 0.950016i \(0.398934\pi\)
\(434\) 1.78514e11 0.241529
\(435\) −2.09071e12 −2.79958
\(436\) −4.09458e10 −0.0542650
\(437\) 9.56917e10 0.125519
\(438\) −2.04151e11 −0.265043
\(439\) 2.27163e11 0.291909 0.145954 0.989291i \(-0.453375\pi\)
0.145954 + 0.989291i \(0.453375\pi\)
\(440\) 4.98314e11 0.633820
\(441\) −6.59347e11 −0.830119
\(442\) 0 0
\(443\) 1.03387e12 1.27541 0.637706 0.770280i \(-0.279883\pi\)
0.637706 + 0.770280i \(0.279883\pi\)
\(444\) 1.48304e11 0.181105
\(445\) 7.35595e11 0.889239
\(446\) −6.57271e11 −0.786571
\(447\) 7.54094e11 0.893392
\(448\) −2.22560e11 −0.261033
\(449\) 1.06299e12 1.23430 0.617150 0.786845i \(-0.288287\pi\)
0.617150 + 0.786845i \(0.288287\pi\)
\(450\) −1.95935e12 −2.25245
\(451\) 1.79264e11 0.204032
\(452\) −6.13406e10 −0.0691233
\(453\) −1.60959e12 −1.79587
\(454\) 8.20712e11 0.906649
\(455\) 8.26044e11 0.903549
\(456\) −2.87272e11 −0.311137
\(457\) −8.26432e10 −0.0886307 −0.0443154 0.999018i \(-0.514111\pi\)
−0.0443154 + 0.999018i \(0.514111\pi\)
\(458\) −8.21980e10 −0.0872904
\(459\) 0 0
\(460\) 1.13805e11 0.118509
\(461\) 1.90976e11 0.196936 0.0984680 0.995140i \(-0.468606\pi\)
0.0984680 + 0.995140i \(0.468606\pi\)
\(462\) −1.66864e11 −0.170402
\(463\) 9.16066e11 0.926429 0.463214 0.886246i \(-0.346696\pi\)
0.463214 + 0.886246i \(0.346696\pi\)
\(464\) −1.23071e12 −1.23261
\(465\) −1.87238e12 −1.85719
\(466\) 8.32571e11 0.817871
\(467\) 1.75288e12 1.70540 0.852701 0.522400i \(-0.174963\pi\)
0.852701 + 0.522400i \(0.174963\pi\)
\(468\) −1.92209e11 −0.185211
\(469\) −1.05093e11 −0.100299
\(470\) −3.10575e12 −2.93580
\(471\) 2.24834e12 2.10508
\(472\) −9.99162e11 −0.926610
\(473\) −6.45850e11 −0.593276
\(474\) −6.39081e11 −0.581505
\(475\) 6.21616e11 0.560275
\(476\) 0 0
\(477\) 2.80355e11 0.247957
\(478\) −1.64225e12 −1.43885
\(479\) 8.05193e11 0.698860 0.349430 0.936963i \(-0.386375\pi\)
0.349430 + 0.936963i \(0.386375\pi\)
\(480\) −7.32385e11 −0.629730
\(481\) 1.96331e12 1.67239
\(482\) −6.90395e11 −0.582620
\(483\) 2.65245e11 0.221761
\(484\) −1.30295e11 −0.107925
\(485\) 7.19679e11 0.590610
\(486\) −1.79476e12 −1.45929
\(487\) 2.02412e11 0.163063 0.0815315 0.996671i \(-0.474019\pi\)
0.0815315 + 0.996671i \(0.474019\pi\)
\(488\) 2.19551e12 1.75245
\(489\) −1.37275e12 −1.08568
\(490\) 2.22912e12 1.74683
\(491\) −1.40366e12 −1.08992 −0.544960 0.838462i \(-0.683455\pi\)
−0.544960 + 0.838462i \(0.683455\pi\)
\(492\) −1.22905e11 −0.0945645
\(493\) 0 0
\(494\) 5.46393e11 0.412794
\(495\) 8.37557e11 0.627034
\(496\) −1.10219e12 −0.817692
\(497\) −2.62362e11 −0.192884
\(498\) −1.91583e12 −1.39581
\(499\) 1.34731e12 0.972784 0.486392 0.873741i \(-0.338313\pi\)
0.486392 + 0.873741i \(0.338313\pi\)
\(500\) 4.19708e11 0.300319
\(501\) 1.84863e12 1.31093
\(502\) −1.21973e12 −0.857228
\(503\) 9.70190e11 0.675773 0.337887 0.941187i \(-0.390288\pi\)
0.337887 + 0.941187i \(0.390288\pi\)
\(504\) −3.81062e11 −0.263062
\(505\) 5.61816e11 0.384400
\(506\) −3.04340e11 −0.206386
\(507\) −3.25687e12 −2.18910
\(508\) 3.47378e11 0.231428
\(509\) −4.58129e11 −0.302523 −0.151261 0.988494i \(-0.548334\pi\)
−0.151261 + 0.988494i \(0.548334\pi\)
\(510\) 0 0
\(511\) 8.59139e10 0.0557403
\(512\) 1.16980e12 0.752311
\(513\) 4.32785e10 0.0275895
\(514\) −1.06580e12 −0.673506
\(515\) −2.68023e11 −0.167896
\(516\) 4.42802e11 0.274970
\(517\) 9.26920e11 0.570604
\(518\) −5.59224e11 −0.341273
\(519\) 2.62039e12 1.58531
\(520\) −4.52291e12 −2.71271
\(521\) 9.79258e11 0.582274 0.291137 0.956681i \(-0.405966\pi\)
0.291137 + 0.956681i \(0.405966\pi\)
\(522\) −1.83442e12 −1.08139
\(523\) −1.82449e12 −1.06631 −0.533157 0.846016i \(-0.678994\pi\)
−0.533157 + 0.846016i \(0.678994\pi\)
\(524\) −1.77904e11 −0.103085
\(525\) 1.72304e12 0.989869
\(526\) −1.06927e12 −0.609048
\(527\) 0 0
\(528\) 1.03026e12 0.576892
\(529\) −1.31738e12 −0.731409
\(530\) −9.47823e11 −0.521778
\(531\) −1.67937e12 −0.916689
\(532\) −1.73693e10 −0.00940110
\(533\) −1.62708e12 −0.873243
\(534\) 1.34869e12 0.717757
\(535\) −1.26368e12 −0.666876
\(536\) 5.75425e11 0.301125
\(537\) 4.51046e12 2.34065
\(538\) 1.86207e12 0.958242
\(539\) −6.65286e11 −0.339515
\(540\) 5.14706e10 0.0260488
\(541\) 2.54541e12 1.27753 0.638763 0.769403i \(-0.279446\pi\)
0.638763 + 0.769403i \(0.279446\pi\)
\(542\) −4.91502e11 −0.244641
\(543\) 2.03230e12 1.00320
\(544\) 0 0
\(545\) −1.61944e12 −0.786285
\(546\) 1.51453e12 0.729307
\(547\) 7.76701e11 0.370946 0.185473 0.982649i \(-0.440618\pi\)
0.185473 + 0.982649i \(0.440618\pi\)
\(548\) −1.96844e11 −0.0932417
\(549\) 3.69018e12 1.73369
\(550\) −1.97700e12 −0.921243
\(551\) 5.81981e11 0.268984
\(552\) −1.45232e12 −0.665788
\(553\) 2.68948e11 0.122294
\(554\) 2.19258e12 0.988922
\(555\) 5.86553e12 2.62415
\(556\) 2.28361e11 0.101341
\(557\) 1.13490e12 0.499586 0.249793 0.968299i \(-0.419637\pi\)
0.249793 + 0.968299i \(0.419637\pi\)
\(558\) −1.64285e12 −0.717373
\(559\) 5.86201e12 2.53918
\(560\) 1.45273e12 0.624221
\(561\) 0 0
\(562\) −3.81824e12 −1.61455
\(563\) 6.84519e11 0.287143 0.143571 0.989640i \(-0.454141\pi\)
0.143571 + 0.989640i \(0.454141\pi\)
\(564\) −6.35507e11 −0.264463
\(565\) −2.42607e12 −1.00158
\(566\) 1.18548e12 0.485534
\(567\) 8.17853e11 0.332316
\(568\) 1.43653e12 0.579092
\(569\) 4.27388e11 0.170930 0.0854648 0.996341i \(-0.472762\pi\)
0.0854648 + 0.996341i \(0.472762\pi\)
\(570\) 1.63239e12 0.647719
\(571\) 3.34538e12 1.31699 0.658496 0.752584i \(-0.271193\pi\)
0.658496 + 0.752584i \(0.271193\pi\)
\(572\) −1.93941e11 −0.0757507
\(573\) −5.57397e12 −2.16008
\(574\) 4.63451e11 0.178197
\(575\) 3.14261e12 1.19891
\(576\) 2.04820e12 0.775303
\(577\) −6.11445e10 −0.0229650 −0.0114825 0.999934i \(-0.503655\pi\)
−0.0114825 + 0.999934i \(0.503655\pi\)
\(578\) 0 0
\(579\) 2.05233e11 0.0758914
\(580\) 6.92143e11 0.253963
\(581\) 8.06251e11 0.293547
\(582\) 1.31951e12 0.476716
\(583\) 2.82881e11 0.101413
\(584\) −4.70412e11 −0.167348
\(585\) −7.60202e12 −2.68366
\(586\) −2.27202e12 −0.795925
\(587\) −1.97678e12 −0.687206 −0.343603 0.939115i \(-0.611648\pi\)
−0.343603 + 0.939115i \(0.611648\pi\)
\(588\) 4.56128e11 0.157358
\(589\) 5.21206e11 0.178439
\(590\) 5.67761e12 1.92900
\(591\) −2.89337e11 −0.0975573
\(592\) 3.45279e12 1.15537
\(593\) −2.58955e12 −0.859959 −0.429980 0.902839i \(-0.641479\pi\)
−0.429980 + 0.902839i \(0.641479\pi\)
\(594\) −1.37644e11 −0.0453646
\(595\) 0 0
\(596\) −2.49648e11 −0.0810438
\(597\) 2.43921e12 0.785894
\(598\) 2.76232e12 0.883320
\(599\) 2.28277e12 0.724507 0.362253 0.932080i \(-0.382008\pi\)
0.362253 + 0.932080i \(0.382008\pi\)
\(600\) −9.43429e12 −2.97186
\(601\) 3.16197e12 0.988603 0.494302 0.869290i \(-0.335424\pi\)
0.494302 + 0.869290i \(0.335424\pi\)
\(602\) −1.66972e12 −0.518154
\(603\) 9.67163e11 0.297901
\(604\) 5.32866e11 0.162912
\(605\) −5.15325e12 −1.56380
\(606\) 1.03007e12 0.310271
\(607\) 2.56502e12 0.766906 0.383453 0.923560i \(-0.374735\pi\)
0.383453 + 0.923560i \(0.374735\pi\)
\(608\) 2.03870e11 0.0605046
\(609\) 1.61317e12 0.475229
\(610\) −1.24757e13 −3.64822
\(611\) −8.41312e12 −2.44215
\(612\) 0 0
\(613\) −1.33870e12 −0.382923 −0.191461 0.981500i \(-0.561323\pi\)
−0.191461 + 0.981500i \(0.561323\pi\)
\(614\) −4.58630e12 −1.30228
\(615\) −4.86100e12 −1.37021
\(616\) −3.84495e11 −0.107591
\(617\) 3.94532e11 0.109597 0.0547985 0.998497i \(-0.482548\pi\)
0.0547985 + 0.998497i \(0.482548\pi\)
\(618\) −4.91412e11 −0.135518
\(619\) 4.29120e12 1.17482 0.587410 0.809290i \(-0.300148\pi\)
0.587410 + 0.809290i \(0.300148\pi\)
\(620\) 6.19864e11 0.168474
\(621\) 2.18796e11 0.0590375
\(622\) 4.37743e12 1.17264
\(623\) −5.67579e11 −0.150949
\(624\) −9.35109e12 −2.46906
\(625\) 7.77509e12 2.03819
\(626\) −5.20548e12 −1.35480
\(627\) −4.87191e11 −0.125891
\(628\) −7.44330e11 −0.190962
\(629\) 0 0
\(630\) 2.16534e12 0.547638
\(631\) −2.10436e12 −0.528431 −0.264215 0.964464i \(-0.585113\pi\)
−0.264215 + 0.964464i \(0.585113\pi\)
\(632\) −1.47259e12 −0.367161
\(633\) −5.89735e12 −1.45996
\(634\) −5.74481e12 −1.41213
\(635\) 1.37391e13 3.35332
\(636\) −1.93946e11 −0.0470028
\(637\) 6.03842e12 1.45310
\(638\) −1.85094e12 −0.442282
\(639\) 2.41450e12 0.572892
\(640\) −8.85459e12 −2.08621
\(641\) −4.70391e12 −1.10052 −0.550260 0.834993i \(-0.685472\pi\)
−0.550260 + 0.834993i \(0.685472\pi\)
\(642\) −2.31692e12 −0.538275
\(643\) −2.97950e12 −0.687376 −0.343688 0.939084i \(-0.611676\pi\)
−0.343688 + 0.939084i \(0.611676\pi\)
\(644\) −8.78111e10 −0.0201170
\(645\) 1.75132e13 3.98424
\(646\) 0 0
\(647\) −6.15794e11 −0.138155 −0.0690774 0.997611i \(-0.522006\pi\)
−0.0690774 + 0.997611i \(0.522006\pi\)
\(648\) −4.47806e12 −0.997706
\(649\) −1.69450e12 −0.374922
\(650\) 1.79441e13 3.94285
\(651\) 1.44471e12 0.315259
\(652\) 4.54458e11 0.0984871
\(653\) −6.22513e12 −1.33980 −0.669899 0.742453i \(-0.733662\pi\)
−0.669899 + 0.742453i \(0.733662\pi\)
\(654\) −2.96919e12 −0.634656
\(655\) −7.03624e12 −1.49367
\(656\) −2.86147e12 −0.603284
\(657\) −7.90660e11 −0.165556
\(658\) 2.39637e12 0.498353
\(659\) 5.49448e12 1.13486 0.567430 0.823421i \(-0.307938\pi\)
0.567430 + 0.823421i \(0.307938\pi\)
\(660\) −5.79411e11 −0.118861
\(661\) −2.29988e11 −0.0468596 −0.0234298 0.999725i \(-0.507459\pi\)
−0.0234298 + 0.999725i \(0.507459\pi\)
\(662\) 6.46976e12 1.30926
\(663\) 0 0
\(664\) −4.41454e12 −0.881310
\(665\) −6.86967e11 −0.136219
\(666\) 5.14650e12 1.01363
\(667\) 2.94223e12 0.575586
\(668\) −6.12002e11 −0.118921
\(669\) −5.31929e12 −1.02668
\(670\) −3.26978e12 −0.626876
\(671\) 3.72342e12 0.709072
\(672\) 5.65102e11 0.106897
\(673\) −9.70100e11 −0.182284 −0.0911420 0.995838i \(-0.529052\pi\)
−0.0911420 + 0.995838i \(0.529052\pi\)
\(674\) −4.53401e12 −0.846277
\(675\) 1.42131e12 0.263524
\(676\) 1.07821e12 0.198584
\(677\) 5.03955e12 0.922026 0.461013 0.887393i \(-0.347486\pi\)
0.461013 + 0.887393i \(0.347486\pi\)
\(678\) −4.44813e12 −0.808432
\(679\) −5.55298e11 −0.100256
\(680\) 0 0
\(681\) 6.64201e12 1.18342
\(682\) −1.65765e12 −0.293402
\(683\) 5.01528e12 0.881864 0.440932 0.897540i \(-0.354648\pi\)
0.440932 + 0.897540i \(0.354648\pi\)
\(684\) 1.59848e11 0.0279225
\(685\) −7.78534e12 −1.35105
\(686\) −3.62148e12 −0.624349
\(687\) −6.65227e11 −0.113937
\(688\) 1.03093e13 1.75420
\(689\) −2.56754e12 −0.434042
\(690\) 8.25261e12 1.38602
\(691\) 2.82622e12 0.471580 0.235790 0.971804i \(-0.424232\pi\)
0.235790 + 0.971804i \(0.424232\pi\)
\(692\) −8.67498e11 −0.143811
\(693\) −6.46252e11 −0.106439
\(694\) 4.07203e12 0.666336
\(695\) 9.03187e12 1.46841
\(696\) −8.83275e12 −1.42677
\(697\) 0 0
\(698\) 7.32369e12 1.16783
\(699\) 6.73799e12 1.06754
\(700\) −5.70423e11 −0.0897958
\(701\) 2.11841e12 0.331343 0.165672 0.986181i \(-0.447021\pi\)
0.165672 + 0.986181i \(0.447021\pi\)
\(702\) 1.24931e12 0.194157
\(703\) −1.63276e12 −0.252129
\(704\) 2.06665e12 0.317095
\(705\) −2.51348e13 −3.83199
\(706\) 3.57137e11 0.0541021
\(707\) −4.33492e11 −0.0652520
\(708\) 1.16177e12 0.173768
\(709\) −1.08197e13 −1.60808 −0.804039 0.594576i \(-0.797320\pi\)
−0.804039 + 0.594576i \(0.797320\pi\)
\(710\) −8.16291e12 −1.20554
\(711\) −2.47511e12 −0.363230
\(712\) 3.10771e12 0.453190
\(713\) 2.63498e12 0.381834
\(714\) 0 0
\(715\) −7.67050e12 −1.09761
\(716\) −1.49322e12 −0.212332
\(717\) −1.32907e13 −1.87808
\(718\) 1.95387e12 0.274369
\(719\) 2.57986e12 0.360011 0.180006 0.983666i \(-0.442388\pi\)
0.180006 + 0.983666i \(0.442388\pi\)
\(720\) −1.33694e13 −1.85402
\(721\) 2.06804e11 0.0285004
\(722\) 7.29225e12 0.998721
\(723\) −5.58736e12 −0.760473
\(724\) −6.72806e11 −0.0910052
\(725\) 1.91128e13 2.56923
\(726\) −9.44834e12 −1.26224
\(727\) −4.66836e11 −0.0619811 −0.0309905 0.999520i \(-0.509866\pi\)
−0.0309905 + 0.999520i \(0.509866\pi\)
\(728\) 3.48984e12 0.460483
\(729\) −6.32368e12 −0.829271
\(730\) 2.67306e12 0.348381
\(731\) 0 0
\(732\) −2.55282e12 −0.328639
\(733\) −8.68081e12 −1.11069 −0.555344 0.831621i \(-0.687414\pi\)
−0.555344 + 0.831621i \(0.687414\pi\)
\(734\) 6.63302e12 0.843488
\(735\) 1.80402e13 2.28007
\(736\) 1.03068e12 0.129471
\(737\) 9.75875e11 0.121840
\(738\) −4.26511e12 −0.529269
\(739\) 1.36517e13 1.68379 0.841894 0.539643i \(-0.181441\pi\)
0.841894 + 0.539643i \(0.181441\pi\)
\(740\) −1.94182e12 −0.238049
\(741\) 4.42195e12 0.538805
\(742\) 7.31332e11 0.0885721
\(743\) −5.41571e12 −0.651937 −0.325968 0.945381i \(-0.605690\pi\)
−0.325968 + 0.945381i \(0.605690\pi\)
\(744\) −7.91036e12 −0.946495
\(745\) −9.87377e12 −1.17430
\(746\) −1.62180e12 −0.191722
\(747\) −7.41987e12 −0.871874
\(748\) 0 0
\(749\) 9.75045e11 0.113203
\(750\) 3.04352e13 3.51237
\(751\) 4.96526e12 0.569590 0.284795 0.958588i \(-0.408074\pi\)
0.284795 + 0.958588i \(0.408074\pi\)
\(752\) −1.47958e13 −1.68717
\(753\) −9.87125e12 −1.11891
\(754\) 1.67999e13 1.89294
\(755\) 2.10753e13 2.36054
\(756\) −3.97143e10 −0.00442179
\(757\) 1.38118e13 1.52869 0.764343 0.644810i \(-0.223064\pi\)
0.764343 + 0.644810i \(0.223064\pi\)
\(758\) −5.48631e11 −0.0603627
\(759\) −2.46302e12 −0.269389
\(760\) 3.76141e12 0.408968
\(761\) 1.56510e13 1.69166 0.845828 0.533455i \(-0.179107\pi\)
0.845828 + 0.533455i \(0.179107\pi\)
\(762\) 2.51902e13 2.70666
\(763\) 1.24954e12 0.133472
\(764\) 1.84530e12 0.195951
\(765\) 0 0
\(766\) −1.29986e13 −1.36417
\(767\) 1.53800e13 1.60464
\(768\) −4.95562e12 −0.514011
\(769\) −4.07932e11 −0.0420648 −0.0210324 0.999779i \(-0.506695\pi\)
−0.0210324 + 0.999779i \(0.506695\pi\)
\(770\) 2.18484e12 0.223981
\(771\) −8.62550e12 −0.879102
\(772\) −6.79436e10 −0.00688447
\(773\) 2.25431e11 0.0227094 0.0113547 0.999936i \(-0.496386\pi\)
0.0113547 + 0.999936i \(0.496386\pi\)
\(774\) 1.53663e13 1.53899
\(775\) 1.71169e13 1.70438
\(776\) 3.04047e12 0.300998
\(777\) −4.52579e12 −0.445451
\(778\) 5.85578e12 0.573029
\(779\) 1.35313e12 0.131650
\(780\) 5.25898e12 0.508716
\(781\) 2.43625e12 0.234310
\(782\) 0 0
\(783\) 1.33068e12 0.126516
\(784\) 1.06195e13 1.00388
\(785\) −2.94388e13 −2.76698
\(786\) −1.29008e13 −1.20563
\(787\) 1.53299e13 1.42446 0.712232 0.701944i \(-0.247684\pi\)
0.712232 + 0.701944i \(0.247684\pi\)
\(788\) 9.57868e10 0.00884989
\(789\) −8.65359e12 −0.794968
\(790\) 8.36783e12 0.764348
\(791\) 1.87193e12 0.170018
\(792\) 3.53848e12 0.319560
\(793\) −3.37953e13 −3.03478
\(794\) 1.62011e13 1.44661
\(795\) −7.67072e12 −0.681058
\(796\) −8.07516e11 −0.0712922
\(797\) −5.72337e12 −0.502446 −0.251223 0.967929i \(-0.580833\pi\)
−0.251223 + 0.967929i \(0.580833\pi\)
\(798\) −1.25954e12 −0.109951
\(799\) 0 0
\(800\) 6.69530e12 0.577917
\(801\) 5.22338e12 0.448338
\(802\) 9.01117e12 0.769125
\(803\) −7.97781e11 −0.0677117
\(804\) −6.69071e11 −0.0564703
\(805\) −3.47300e12 −0.291489
\(806\) 1.50455e13 1.25574
\(807\) 1.50697e13 1.25076
\(808\) 2.37354e12 0.195905
\(809\) 3.52847e12 0.289613 0.144807 0.989460i \(-0.453744\pi\)
0.144807 + 0.989460i \(0.453744\pi\)
\(810\) 2.54460e13 2.07700
\(811\) 1.52284e13 1.23612 0.618058 0.786133i \(-0.287920\pi\)
0.618058 + 0.786133i \(0.287920\pi\)
\(812\) −5.34052e11 −0.0431103
\(813\) −3.97772e12 −0.319321
\(814\) 5.19286e12 0.414569
\(815\) 1.79742e13 1.42705
\(816\) 0 0
\(817\) −4.87505e12 −0.382807
\(818\) −1.51667e13 −1.18441
\(819\) 5.86565e12 0.455553
\(820\) 1.60927e12 0.124298
\(821\) 2.18898e13 1.68150 0.840752 0.541420i \(-0.182113\pi\)
0.840752 + 0.541420i \(0.182113\pi\)
\(822\) −1.42742e13 −1.09051
\(823\) 1.41049e13 1.07169 0.535846 0.844316i \(-0.319993\pi\)
0.535846 + 0.844316i \(0.319993\pi\)
\(824\) −1.13233e12 −0.0855660
\(825\) −1.59998e13 −1.20246
\(826\) −4.38079e12 −0.327448
\(827\) 1.50447e12 0.111843 0.0559216 0.998435i \(-0.482190\pi\)
0.0559216 + 0.998435i \(0.482190\pi\)
\(828\) 8.08119e11 0.0597501
\(829\) 1.36965e13 1.00720 0.503600 0.863937i \(-0.332009\pi\)
0.503600 + 0.863937i \(0.332009\pi\)
\(830\) 2.50850e13 1.83469
\(831\) 1.77445e13 1.29080
\(832\) −1.87578e13 −1.35715
\(833\) 0 0
\(834\) 1.65597e13 1.18524
\(835\) −2.42051e13 −1.72313
\(836\) 1.61288e11 0.0114202
\(837\) 1.19172e12 0.0839286
\(838\) −1.39638e13 −0.978148
\(839\) −1.29771e12 −0.0904170 −0.0452085 0.998978i \(-0.514395\pi\)
−0.0452085 + 0.998978i \(0.514395\pi\)
\(840\) 1.04261e13 0.722548
\(841\) 3.38699e12 0.233470
\(842\) −8.96649e12 −0.614778
\(843\) −3.09010e13 −2.10741
\(844\) 1.95236e12 0.132440
\(845\) 4.26440e13 2.87742
\(846\) −2.20536e13 −1.48017
\(847\) 3.97620e12 0.265456
\(848\) −4.51543e12 −0.299859
\(849\) 9.59407e12 0.633750
\(850\) 0 0
\(851\) −8.25450e12 −0.539520
\(852\) −1.67032e12 −0.108598
\(853\) 8.68335e12 0.561587 0.280793 0.959768i \(-0.409402\pi\)
0.280793 + 0.959768i \(0.409402\pi\)
\(854\) 9.62615e12 0.619288
\(855\) 6.32211e12 0.404589
\(856\) −5.33875e12 −0.339866
\(857\) 1.27598e13 0.808034 0.404017 0.914751i \(-0.367614\pi\)
0.404017 + 0.914751i \(0.367614\pi\)
\(858\) −1.40636e13 −0.885942
\(859\) 2.56569e12 0.160781 0.0803905 0.996763i \(-0.474383\pi\)
0.0803905 + 0.996763i \(0.474383\pi\)
\(860\) −5.79785e12 −0.361430
\(861\) 3.75071e12 0.232594
\(862\) −3.17171e13 −1.95664
\(863\) −2.29743e13 −1.40992 −0.704960 0.709247i \(-0.749035\pi\)
−0.704960 + 0.709247i \(0.749035\pi\)
\(864\) 4.66144e11 0.0284582
\(865\) −3.43102e13 −2.08378
\(866\) −1.09646e13 −0.662461
\(867\) 0 0
\(868\) −4.78282e11 −0.0285986
\(869\) −2.49740e12 −0.148559
\(870\) 5.01910e13 2.97022
\(871\) −8.85745e12 −0.521467
\(872\) −6.84173e12 −0.400721
\(873\) 5.11037e12 0.297775
\(874\) −2.29724e12 −0.133169
\(875\) −1.28082e13 −0.738674
\(876\) 5.46968e11 0.0313829
\(877\) −2.71354e13 −1.54895 −0.774475 0.632604i \(-0.781986\pi\)
−0.774475 + 0.632604i \(0.781986\pi\)
\(878\) −5.45342e12 −0.309702
\(879\) −1.83874e13 −1.03889
\(880\) −1.34898e13 −0.758285
\(881\) −8.69256e12 −0.486134 −0.243067 0.970009i \(-0.578154\pi\)
−0.243067 + 0.970009i \(0.578154\pi\)
\(882\) 1.58287e13 0.880719
\(883\) 1.44572e13 0.800318 0.400159 0.916446i \(-0.368955\pi\)
0.400159 + 0.916446i \(0.368955\pi\)
\(884\) 0 0
\(885\) 4.59488e13 2.51785
\(886\) −2.48199e13 −1.35315
\(887\) −2.51921e13 −1.36649 −0.683246 0.730188i \(-0.739433\pi\)
−0.683246 + 0.730188i \(0.739433\pi\)
\(888\) 2.47805e13 1.33737
\(889\) −1.06009e13 −0.569228
\(890\) −1.76592e13 −0.943442
\(891\) −7.59444e12 −0.403688
\(892\) 1.76099e12 0.0931352
\(893\) 6.99664e12 0.368178
\(894\) −1.81033e13 −0.947848
\(895\) −5.90579e13 −3.07662
\(896\) 6.83213e12 0.354136
\(897\) 2.23554e13 1.15296
\(898\) −2.55188e13 −1.30954
\(899\) 1.60255e13 0.818263
\(900\) 5.24956e12 0.266705
\(901\) 0 0
\(902\) −4.30353e12 −0.216469
\(903\) −1.35130e13 −0.676327
\(904\) −1.02495e13 −0.510442
\(905\) −2.66100e13 −1.31864
\(906\) 3.86409e13 1.90533
\(907\) 3.05227e13 1.49758 0.748790 0.662807i \(-0.230635\pi\)
0.748790 + 0.662807i \(0.230635\pi\)
\(908\) −2.19888e12 −0.107353
\(909\) 3.98940e12 0.193807
\(910\) −1.98306e13 −0.958625
\(911\) 3.56835e13 1.71646 0.858231 0.513264i \(-0.171564\pi\)
0.858231 + 0.513264i \(0.171564\pi\)
\(912\) 7.77669e12 0.372236
\(913\) −7.48671e12 −0.356593
\(914\) 1.98399e12 0.0940331
\(915\) −1.00966e14 −4.76189
\(916\) 2.20228e11 0.0103358
\(917\) 5.42910e12 0.253551
\(918\) 0 0
\(919\) −2.57192e13 −1.18943 −0.594713 0.803938i \(-0.702734\pi\)
−0.594713 + 0.803938i \(0.702734\pi\)
\(920\) 1.90160e13 0.875132
\(921\) −3.71169e13 −1.69982
\(922\) −4.58470e12 −0.208940
\(923\) −2.21124e13 −1.00283
\(924\) 4.47068e11 0.0201767
\(925\) −5.36214e13 −2.40824
\(926\) −2.19917e13 −0.982899
\(927\) −1.90320e12 −0.0846498
\(928\) 6.26840e12 0.277454
\(929\) −4.15886e12 −0.183191 −0.0915953 0.995796i \(-0.529197\pi\)
−0.0915953 + 0.995796i \(0.529197\pi\)
\(930\) 4.49496e13 1.97039
\(931\) −5.02176e12 −0.219070
\(932\) −2.23066e12 −0.0968414
\(933\) 3.54265e13 1.53060
\(934\) −4.20808e13 −1.80935
\(935\) 0 0
\(936\) −3.21167e13 −1.36770
\(937\) 9.33151e12 0.395479 0.197740 0.980255i \(-0.436640\pi\)
0.197740 + 0.980255i \(0.436640\pi\)
\(938\) 2.52293e12 0.106412
\(939\) −4.21279e13 −1.76838
\(940\) 8.32104e12 0.347618
\(941\) −2.25028e13 −0.935585 −0.467792 0.883838i \(-0.654950\pi\)
−0.467792 + 0.883838i \(0.654950\pi\)
\(942\) −5.39752e13 −2.23339
\(943\) 6.84083e12 0.281713
\(944\) 2.70481e13 1.10857
\(945\) −1.57073e12 −0.0640706
\(946\) 1.55047e13 0.629438
\(947\) −7.23383e11 −0.0292276 −0.0146138 0.999893i \(-0.504652\pi\)
−0.0146138 + 0.999893i \(0.504652\pi\)
\(948\) 1.71225e12 0.0688540
\(949\) 7.24100e12 0.289802
\(950\) −1.49229e13 −0.594426
\(951\) −4.64927e13 −1.84320
\(952\) 0 0
\(953\) 4.77982e13 1.87713 0.938563 0.345107i \(-0.112157\pi\)
0.938563 + 0.345107i \(0.112157\pi\)
\(954\) −6.73039e12 −0.263071
\(955\) 7.29830e13 2.83927
\(956\) 4.39999e12 0.170369
\(957\) −1.49796e13 −0.577295
\(958\) −1.93300e13 −0.741458
\(959\) 6.00710e12 0.229341
\(960\) −5.60402e13 −2.12951
\(961\) −1.20876e13 −0.457179
\(962\) −4.71326e13 −1.77433
\(963\) −8.97327e12 −0.336227
\(964\) 1.84973e12 0.0689862
\(965\) −2.68722e12 −0.0997541
\(966\) −6.36764e12 −0.235278
\(967\) −3.15015e13 −1.15854 −0.579272 0.815134i \(-0.696663\pi\)
−0.579272 + 0.815134i \(0.696663\pi\)
\(968\) −2.17712e13 −0.796974
\(969\) 0 0
\(970\) −1.72771e13 −0.626611
\(971\) 6.67606e12 0.241009 0.120505 0.992713i \(-0.461549\pi\)
0.120505 + 0.992713i \(0.461549\pi\)
\(972\) 4.80859e12 0.172790
\(973\) −6.96891e12 −0.249263
\(974\) −4.85923e12 −0.173002
\(975\) 1.45221e14 5.14646
\(976\) −5.94343e13 −2.09659
\(977\) −4.15163e13 −1.45778 −0.728891 0.684630i \(-0.759964\pi\)
−0.728891 + 0.684630i \(0.759964\pi\)
\(978\) 3.29551e13 1.15186
\(979\) 5.27043e12 0.183368
\(980\) −5.97233e12 −0.206836
\(981\) −1.14995e13 −0.396430
\(982\) 3.36971e13 1.15635
\(983\) −9.03604e12 −0.308665 −0.154333 0.988019i \(-0.549323\pi\)
−0.154333 + 0.988019i \(0.549323\pi\)
\(984\) −2.05366e13 −0.698313
\(985\) 3.78844e12 0.128232
\(986\) 0 0
\(987\) 1.93938e13 0.650482
\(988\) −1.46392e12 −0.0488776
\(989\) −2.46461e13 −0.819151
\(990\) −2.01069e13 −0.665254
\(991\) 3.19314e13 1.05169 0.525844 0.850581i \(-0.323749\pi\)
0.525844 + 0.850581i \(0.323749\pi\)
\(992\) 5.61380e12 0.184058
\(993\) 5.23597e13 1.70894
\(994\) 6.29843e12 0.204641
\(995\) −3.19379e13 −1.03300
\(996\) 5.13297e12 0.165273
\(997\) 3.11747e13 0.999248 0.499624 0.866242i \(-0.333471\pi\)
0.499624 + 0.866242i \(0.333471\pi\)
\(998\) −3.23445e13 −1.03208
\(999\) −3.73326e12 −0.118589
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 289.10.a.i.1.15 52
17.5 odd 16 17.10.d.a.8.10 52
17.7 odd 16 17.10.d.a.15.10 yes 52
17.16 even 2 inner 289.10.a.i.1.16 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.d.a.8.10 52 17.5 odd 16
17.10.d.a.15.10 yes 52 17.7 odd 16
289.10.a.i.1.15 52 1.1 even 1 trivial
289.10.a.i.1.16 52 17.16 even 2 inner